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arXiv:1512.06102 · Physical review. B./Physical review. B

Spectral function of the two-dimensional Hubbard model: A density matrix renormalization group plus cluster perturbation theory study

Chun Yang, Adrian E. Feiguin

Published Feb 24, 2016• 30 citations
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Abstract

We study the spectral function of the two-dimensional Hubbard model using cluster perturbation theory, and a density matrix renormalization group as a cluster solver. We reconstruct the two-dimensional dispersion at and away from half-filling using $2\ifmmode\times\else\texttimes\fi{}L$ ladders, with $L$ up to 80 sites, yielding results with unprecedented resolution in excellent agreement with quantum Monte Carlo. The main features of the spectrum can be described with a mean-field dispersion, with kinks and pseudogap traced back to scattering between spin and charge degrees of freedom.

DOI
10.1103/physrevb.93.081107

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We study the spectral function of the two-dimensional Hubbard model using cluster perturbation theory, and a density matrix renormalization group as a cluster solver. We reconstruct the two-dimensional dispersion at and away from half-filling using 2\ifmmode×\else\texttimes\fiL2\ifmmode\times\else\texttimes\fi{}L2\ifmmode×\else\texttimes\fiL ladders, with LLL up to 80 sites, yielding results with unprecedented resolution in excellent agreement with quantum Monte Carlo. The main features of the spectrum can be described with a mean-field dispersion, with kinks and pseudogap traced back to scattering between spin and charge degrees of freedom.
We calculate the photoemission spectral function of the one-dimensional Hubbard model away from half filling using the dynamical density-matrix renormalization group method. An approach for calculating momentum-dependent quantities in finite open chains is presented. Comparison with exact Bethe ansatz results demonstrates the unprecedented accuracy of our method. Our results show that the photoemission spectrum of the quasi-one-dimensional conductor TTF-TCNQ provides evidence for spin-charge separation on the scale of the conduction bandwidth.
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Using a Green's-function equation of motion approach the two-dimensional Hubbard model is studied. The decoupling of the hierarchy is performed according to the conserving of the first four spectral moments. Beyond the Roth's two-pole approximation, the damping effect occurs naturally. The energy dispersions at various fillings, the spectral weight, and the density of states are calculated. Comparisons with the quantum Monte Carlo results and the cluster perturbation theory show that our approach can capture some essential features of the Hubbard model.
We calculate the spectral weight of the one- and two-dimensional Hubbard models by performing exact diagonalizations of finite clusters and treating intercluster hopping with perturbation theory. Even with relatively modest clusters (e.g., 12 sites), the spectra thus obtained give an accurate description of the exact results. Spin-charge separation (i.e., an extended spectral weight bounded by singularities dispersing with wave vector) is clearly recognized in the one-dimensional Hubbard model, and so is extended spectral weight in the two-dimensional Hubbard model.
Using a Green's-function equation of motion approach the two-dimensional Hubbard model is studied. The decoupling of the hierarchy is performed according to the conserving of the first four spectral moments. Beyond the Roth's two-pole approximation, the damping effect occurs naturally. The energy dispersions at various fillings, the spectral weight, and the density of states are calculated. Comparisons with the quantum Monte Carlo results and the cluster perturbation theory show that our approach can capture some essential features of the Hubbard model.
We study cluster perturbation theory [Phys. Rev. Lett. 84, 522 (2000)] when auxiliary field quantum Monte Carlo method is used for solving the cluster hamiltonian. As a case study, we calculate the spectral functions of the Hubbard model in one and two dimensions and compare our results for the spectral functions to results obtained using exact diagonalization to solve the cluster hamiltonian. The main advantage of using quantum Monte Carlo results as a starting point is that the initial cluster size can be taken to be considerably larger and hence potentially capture more of the relevant physics. The drawback is that quantum Monte Carlo methods yield results at imaginary times with stochastic errors.